论文标题
从瞬间系统开始的Navier-Stokes方程的边界条件的构建
Construction of boundary conditions for Navier-Stokes equations from the moment system
论文作者
论文摘要
这项工作涉及稀有气体的线性力矩系统的边界条件（BCS）。由于Knudsen数量足够小，我们通过诉诸三尺度的渐近扩展来分析矩系统的边界层行为。渐近分析将流量投入外溶液，粘性层和Knudsen层。从当时系统的BC开始，我们提出了匹配要求，并为Navier-Stokes方程构建BCS。所获得的BC包含二阶项对速度滑移和温度跳跃的影响。对于COUETTE流的说明性情况，我们通过误差估计来证明构建的BCS的有效性。同时，提出了数值测试以显示构造的BC的性能。
This work concerns with boundary conditions (BCs) of the linearized moment system for rarefied gases. As the Knudsen number is sufficiently small, we analyze the boundary-layer behaviors of the moment system by resorting to a three-scale asymptotic expansion. The asymptotic analysis casts the flows into the outer solution, the viscous layer and the Knudsen layer. Starting from the BCs of the moment system, we propose a matching requirement and construct BCs for the Navier-Stokes equations. The obtained BCs contain the effect of second-order terms on the velocity slip and temperature jump. For the illustrative case of the Couette flow, we prove the validity of the constructed BCs through the error estimates. Meanwhile, numerical tests are presented to show the performance of the constructed BCs.
